Submitted Paper
Inserted: 10 oct 2023
Last Updated: 8 apr 2025
Year: 2023
Abstract:
We establish a new class of $L^2$-weighted elliptic estimates on smooth two-manifolds for a family of weights satisfying an equation with explicit constants. This family includes weights that are comparable to the product of positive powers of the geodesic distance to a given collection of points. Our primary motivation is to derive estimates related to a weighted Hodge decomposition for one-forms.
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